NFPA 68 formula 8.3.2 seems to have a fault

The formula uses Kst, Filter Volume & Pred to calculate a pressure developed. This is applied to the number of vents in a system. The idea being to find a weight in Kg/m2 that a deflagration panel may have before the size must be compensated.

Without detailed knowledge of the background of the equation I cannot confirm my hunch that there is a fault but intuitively there seems to be a disconnect in the way the number of panels is applied in the equation (represented by n).

In the equation the number of vents "n" is multiplied through which gives an increase in how much each panel may weigh (kg/m2) with each additional panel in the system. Assuming that the force of the deflagration is constant you would suspect that the forces on each panel would decrease as the number of panels increases and as a result the overall kg/m2 permissible would also decrease. I suspect that the number of panels should be divided into the equation. so "n to the power of 0.3" should in fact be "1/n to the power of 0.3).

I have created a simple excel sheet which demonstrates the use in both cases. The green field is the current formula 8.3.2, the red field is the suggested change. Start be putting n to 1 and increase. You will get the idea. Again this is only a guess at what is wrong, the true fault may lie elsewhere in the formula.

Please note that the formula number refers to the current second draft numbering. In the original 2013 version of the standard the formula was numbered as 8.2.6.2

Mt is the threshold mass above which the inertia factor shall be applied to the vent size equation, increasing the vent size (area), for the simple solution. n is how many panels Av is divided into, equally. Increasing n does not increase Av in the formulas. The committee choose to include Mt believing it would simplify the method. However, Mt can be ignored and the inertial factor can be applied in all cases. Mt was designed to eliminate the application of the inertial factor where the effect is less than 5% (a committee choice). The inertial factor was developed from the FM vent calculation methodology which they graciously gave to the world, with special information provided to the 68 committee. The user is at liberty to use the full FM calculation in the appendix. I used it to develop the simple inertial equation including n^.3; with an eye on the available data. Since we didn't have data to correlate the n factor, I ran a full spectrum of FM calculations and derived the .3 exponent. The inertial factor is essentially a ratio of the speed of the explosion pressure rise to the speed of a panel opening. It gets more complex as it may be in some cases there could be a turbulence reduction by reducing the rate of panel opening. But we have no data or reliable model for that. The committee is very open to updating the Standard 68 based upon new data, models, and suggestions. Thank you for your input.

I had not considered that the rotational velocity was the important factor.

It makes sense that if the rotational velocity is constant and the panel is assumed to be square that a new panel of half the area has a longer radius and the torque needed to move it at the velocity will decrease.